In the poll, Cruz is the first choice of 28 percent of Republican primary voters, while Trump gets 26 percent. They're followed by Marco Rubio at 17 percent, John Kasich at 11 percent, Ben Carson at 10 percent and Jeb Bush at 4 percent.

NBC News

The results from the poll — conducted after Trump's victory in New Hampshire and Saturday's GOP debate in South Carolina — are a significant reversal from last month, when Trump held a 13-point lead over Cruz, 33 percent to 20 percent.

Republican pollster Bill McInturff, who conducted this survey with Democratic pollster Peter Hart and his firm Hart Research Associates, says Trump's drop could signal being "right on top of a shift in the campaign."

"When you see a number this different, it means you might be right on top of a shift in the campaign. What you don't know yet is if the change is going to take place or if it is a momentary 'pause' before the numbers snap back into place," he said.

McInturff added, "So, one poll post-Saturday debate can only reflect there may have been a 'pause' as Republican voters take another look at Trump. This happened earlier this summer and he bounced back stronger. We will have to wait this time and see what voters decide."

This poll comes after other surveys — both nationally and in South Carolina, the site of Saturday's next Republican contest — show Trump with a commanding lead. But some of those weren't conducted entirely after the last debate like the NBC/WSJ poll.

Cruz Talks to NBC News About Facing off With Trump, Uniting Conservatives3:29

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Another possible explanation for Trump's decline in the new NBC/WSJ poll is an increase in "very conservative" Republican voters from January's sample.

If the current poll is re-weighted to reflect the ideological composition from last month, the GOP horserace numbers are: Trump 26 percent, Cruz 25 percent, Rubio 18 percent and Kasich 13 percent — so Trump is ahead by one point, but still down from January.

In addition to Trump's decline in the GOP race, the new NBC/WSJ poll shows a nine-point drop in the percentage of GOP primary voters who can see themselves supporting the real-estate mogul — from 65 percent in January to 56 percent now.